Periodic three-dimensional mesh generation for crystalline aggregates based on Voronoi tessellations

In this paper a method for the generation of three-dimensional periodic meshes for the numerical simulation of polycrystalline aggregates is presented. The mesh construction is based on Voronoi and Hardcore Voronoi tessellations of random point seeds. Special emphasis is paid on the periodicity of the mesh topologies which leads to favorable numerical properties for the determination of effective properties using unit cells. The mesh generation algorithm is able to produce high quality meshes at low computational costs. Based on unit cell simulations with different but statistically equivalent microstructures, the effective linear elastic properties of polycrystals consisting of grains with a cubic symmetry are determined. The numerical results are compared with first-, third- and fifth-order bounds and experimental data. Numerical simulations show the efficiency of the proposed homogenization technique.